Complex numbers

Simplify the complex numbers in term of i.

z= (1+3i)/(1-4i)

Expert Solution

Multiply numerator and denominator by the complex conjugate of the denominator (1+4i).

(1+3i)/(1-4i) ×(1+4i)/(1+4i)

=[ (1+3i)×(1+4i)] /[(1)^2-(4i)^2]

=(1+7i+12i^2)/(1-16i^2)

Take. i^2=-1

= (1+7i+12(-1))/(1-16(-1))

=(7i-11)/17

Or z= 7i/17-11/17

After simplify we will get

z=7/17i-11/17

Nitish Mishra answered 3 years ago

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